Apparatus and method for optical raster-scanning in a micromechanical system

ABSTRACT

A method of operating a micromechanical scanning apparatus includes the steps of identifying a radius of curvature value for a micromechanical mirror and modifying a laser beam to compensate for the radius of curvature value. The identifying step includes the steps of measuring the far-field optical beam radius of a laser beam reflected from the micromechanical mirror. The measured far-field optical beam radius is then divided by a theoretical far-field optical beam radius reflected from an ideal mirror to yield a ratio value M. An analytical expression for M is curve-fitted to experimental data for M with the focal-length as a fitting parameter. The focal-length value determined by this procedure, resulting in a good fit between the analytical curve and the experimental data, is equal to half the radius of curvature of the micromechanical mirror. The micromechanical scanning apparatus is operated by controlling the oscillatory motion of a first micromechanical mirror with a first micromechanical spring and regulating the oscillatory motion of a second micromechanical mirror with a second micromechanical spring.

[0001] The development of the technology described herein was supportedby NSF Grant No. EEC-96-15774 for the study of high-speed,high-resolution micro-optical scanners. The U.S. Government may havecertain rights in this technology.

BRIEF DESCRIPTIONS OF THE INVENTION

[0002] This invention relates generally to optical scanners anddisplays. More particularly, this invention relates to an opticalraster-scanning microelectromechanical system.

BACKGROUND OF THE INVENTION

[0003] Scanning micromirrors fabricated using surface-micromachiningtechnology are known in the art. As used herein, a micromirror, amicroscopic device, a micromachined device, a micromechanical device, ora microelectromechanical device refers to a device with a thirddimension above a horizontal substrate that is less than approximatelyseveral milli-meters. Such devices are constructed using semiconductorprocessing techniques.

[0004] Scanning micromirrors have numerous advantages over traditionalscanning mirrors. For example, they have smaller size, mass, and powerconsumption, and can be more readily integrated with actuators,electronics, light sources, lenses and other optical elements. Morecomplete integration simplifies packaging, reducing the manufacturingcost. These factors add motivation to the development of microfabricatedscanners. In addition to displays, high-speed, high-resolutionmicrooptical scanners have numerous additional applications in medicine,lithography, printing, data storage and data retrieval.

[0005] U.S. Pat. No. 5,867,297 (the '297 patent) entitled “Apparatus andMethod for Optical Scanning with an Oscillatory MicroelectromechanicalSystem” describes early seminal work in the field of oscillatorymicromirrors. The contents of the 297 patent are expressly incorporatedby reference herein.

[0006] The required system tolerances in a system of the type describedin the '297 patent are extremely high. For example, bending of torsionalhinges causes system wobble, defined as rotation about an axis in themirror plane orthogonal to the primary scan axis. In a two mirror systemincluding a fast mirror and a slow mirror, fast mirror wobble of lessthan 1% of the total deflection angle will cause scan lines to overlapand seriously degrade image quality. In the slow mirror, rotationalerrors known as jitter, attributable to errors in following the drivingsignal, can induce non-uniform line spacing. It would be highlydesirable to establish improved mechanical linkages to enhance mirrorperformance.

[0007] Large mirror diameters and rotational angles, facilitated by atilt-up mirror design, are key to the resolution of a scanning system.Moving a large mirror quickly through a large angle requires high-forceactuators and stiff springs to achieve a high resonant frequency.Mechanically, the image resolution is limited by the number of linesthat the fast mirror can scan during the refresh period of the slowmirror. Optically, the resolution is given by the size, flatness androtational angle of the mirror. Increasing the mirror diameter resultsin higher resolution only if the mirror is flat, or if its curvature isoptically corrected. It would be highly desirable to provide a method ofcharacterizing and correcting static mirror curvature to improve theperformance of an optical raster-scanning system.

SUMMARY OF THE INVENTION

[0008] A method of operating a micromechanical scanning apparatusincludes the steps of identifying a radius of curvature value for amicromechanical mirror and modifying a laser beam to compensate for theradius of curvature value. The identifying step includes the step ofmeasuring the far-field optical beam radius of a laser beam reflectedfrom the micromechanical mirror. The measured far-field optical beamradius is then divided by a theoretical far-field optical beam radiusreflected from an ideal mirror to yield a ratio value M. An analyticalexpression for M is curve-fitted to experimental data for M with thefocal-length as a fitting parameter. The focal-length value determinedby this procedure, resulting in a good fit between the analytical curveand the experimental data, is equal to half the radius of curvature ofthe micromechanical mirror.

[0009] The micromechanical scanning apparatus is operated by controllingthe oscillatory motion of a first micromechanical mirror with a firstmicromechanical spring and regulating the oscillatory motion of a secondmicromechanical mirror with a second micromechanical spring.

[0010] The invention provides an improved optical raster-scanningmicromechanical system. Mirror performance in the system is improvedthrough the technique of characterizing and correcting static mirrorcurvature. Improved mechanical linkages that exploit symmetry reducemirror wobble. A triangular control signal maximizes the linearity ofthe scan.

BRIEF DESCRIPTION OF THE DRAWINGS

[0011] For a better understanding of the invention, reference should bemade to the following detailed description taken in conjunction with theaccompanying drawings, in which:

[0012]FIG. 1 illustrates an optical raster-scanning apparatus inaccordance with an embodiment of the invention.

[0013]FIG. 2 illustrates an optical raster-scanning apparatus inaccordance with another embodiment of the invention.

[0014]FIG. 3 illustrates an optical raster-scanning apparatus inaccordance with still another embodiment of the invention.

[0015]FIG. 4 is a perspective view of a fast mirror for use inaccordance with an embodiment of the invention.

[0016]FIG. 5 is a top view of a spring utilized in accordance with anembodiment of the invention.

[0017]FIG. 6 is a side view of the spring of FIG. 5.

[0018]FIG. 7 is a perspective view of a slow mirror for use inaccordance with an embodiment of the invention.

[0019]FIG. 8 is an enlarged perspective view of a portion of the slowmirror of FIG. 7.

[0020]FIG. 9 illustrates the frequency response of a fast mirrorconstructed in accordance with an embodiment of the invention.

[0021]FIG. 10 illustrates the frequency response of a slow mirrorconstructed in accordance with an embodiment of the invention.

[0022]FIG. 11 illustrates far-field optical effects of a curved mirror;this information is used in accordance with the invention to compensatefor mirror curvature.

[0023]FIG. 12 illustrates the aperture effect of a mirror in thefar-field.

[0024]FIG. 13 illustrates the effect of mirror deformation due to combdrive actuation.

[0025] Like reference numerals refer to corresponding parts throughoutthe drawings.

DETAILED DESCRIPTION OF THE INVENTION

[0026]FIG. 1 is a simplified representation of an optical rasterscanning system 20 constructed in accordance with an embodiment of theinvention. The system 20 processes a laser beam 22 with a first mirror30, implemented as a micromechanical device. The first mirror 30 may bea “fast mirror”, as described below, which pivots about a first axis ofrotation 26, causing first rotational motion, as shown with arrow 28. Asdescribed below, the first rotational motion is achieved by pushing orpulling the bottom edge of the mirror 30.

[0027]FIG. 1 also illustrates a second mirror 24, which is alsoimplemented as a micromechanical device. The second mirror 24 may be a“slow mirror”, as described below, which pivots about a second axis ofrotation 32, causing second rotational motion, as shown with arrow 34.As described below, the second rotational motion is achieved by pushingor pulling the left and right sides of the mirror 24. By controlling themotion of the slow mirror 24 and the fast mirror 30, the laser beam 22is projected onto a screen 36 to establish a predetermined pattern, aswill be discussed further below.

[0028]FIG. 2 is a more detailed depiction of an optical raster scanningsystem 20 in accordance with an embodiment of the invention. The system20 of FIG. 2 has its mirrors 24 and 30 fabricated on a singlesemiconductor substrate 38. A laser 40 generates a laser beam 22, whichpasses through an acousto-optic modulator 42. The laser beam 22 issubsequently directed through a spatial filter 44 and through amechanical shutter 46. Thereafter, in accordance with a feature of theinvention, the laser beam 22 is processed by mirror curvaturecompensation optics 48. The optic assembly 48 operates to compensate formirror curvature features that would otherwise degrade opticalperformance, as discussed in detail below. The laser beam 22 is thencontrolled by the first mirror 30 and the second mirror 24, with thelaser beam 22 output being directed by an output mirror 50. Outputoptics 52 may process the laser beam 22 before it is applied to a camera54 or screen.

[0029] The system of FIG. 3 corresponds to the system of FIG. 2 with twoexceptions. First, in the system of FIG. 3, the mirrors 24 and 30 arenot formed on a single substrate, instead they are individuallyfabricated. Second, imaging optics 60 are used between the first mirror30 and the second mirror 24.

[0030] The micro-mirrors 24 and 30 are synchronized with a modulatedlight source. Modulation of the light source is used to displayinformation with the raster-scanner. Switching the light on-and-offdefines the pixels in the display. Grey-scale images can be generatedwith the use of analog or digital modulation of the light source. Laserdiodes and light-emitting diodes are suitable for this application.Instead of a projection device 54, light from the micro-mirror displaysystem can be projected directly on to the retina of the user.Projection on to the retina eliminates the need for a display screen ina head-mounted display. Such an embodiment reduces the weight and costof the system.

[0031]FIG. 4 illustrates a fast mirror 30 constructed in accordance withan embodiment of the invention. The mirror 30 is positioned within amirror frame 62. Torsional bars 64A, 64B connect the mirror 30 to themirror frame 62. The torsional bars 64 operate in the manner describedin the previously referenced '297 patent. FIG. 4 further illustrates amirror frame lift 66 and a mirror lifter 68. These devices may befabricated and otherwise operate in accordance with prior arttechniques.

[0032] The mirror 30 of FIG. 4 has an associated comb drive 70, which iscontrolled by electrodes 71A, 71B, and 71C. A comb drive central beam 72is driven by the comb drive 70 in a controlled manner. The motion fromthe comb drive central beam 72 is transferred to a mirror slider 73,which pushes or pulls the mirror 30. More particularly, it pushes orpulls the bottom of the mirror 30 to rotate the reflected laser beam.The features discussed in connection with FIG. 4 are consistent withthose described in the '297 patent, with the following exception. Inaccordance with the invention, the comb drive central beam 72 isattached to micromechanical springs 74A and 74B. The springs 74 operateto improve the controlled motion of the mirror 30. In the embodiment ofFIG. 4, the springs 74 are axially aligned with the comb drive centralbeam 72. This configuration has been particularly successful inenhancing the range of motion for the fast mirror 30.

[0033]FIG. 5 is a top view of a spring 74 utilized in accordance with anembodiment of the invention. The spring 74 is attached to the comb drivecentral beam 72. The spring 74 includes two interior beams 82A and 82B,two exterior beams 82C, and 82D, and connecting bars 80A and 80B. Beams82A and 82B are attached to an anchor 84.

[0034]FIG. 6 is a side view of the spring 74 taken along the line 6-6 ofFIG. 5. As shown in FIG. 6, the anchor 84 operates to suspend the spring74 over its substrate 86. In particular, FIG. 6 illustrates that beam82B is attached to the anchor 84, holding the beam 82B and the remainingportion of the spring above the substrate 86.

[0035] Back and forth motion, as illustrated by arrow 90 in FIG. 5,imparted by the comb drive central beam 72 from the comb drive 70 causesthe beams 82 to flex in a controlled manner to improve the resultantmotion imparted to the mirror 30.

[0036]FIG. 7 illustrates a slow mirror 24 positioned on a substrate 90.The slow mirror 24 has torsion bars 92A and 92B respectively positionedat the top and bottom of the mirror 24. A mirror frame 94 supports themirror 24, via the torsion bars 92A and 92B. A mirror frame lift 96 andmirror lifter 98 position the mirror 24 over the substrate 90.

[0037]FIG. 7 also illustrates individual comb drives 100A and 100B. Eachcomb drive 100A and 100B respectively controls an individual comb drivecentral beam 102A and 102B. Each comb drive central beam 102A/102B isattached to a mirror slider. Each mirror slider comprises a firsttransverse member (e.g., 105A), which is transverse to its linked combdrive central beam (e.g., 102A), an aligned member (e.g., 108), which isaligned or parallel with its associated comb drive central beam (e.g.,102A), and a second transverse member (e.g., 110A). The secondtransverse members 110A and 110B are respectively connected to mirrorflanges 112A and 112B.

[0038] The motion of the slow mirror 24 is controlled by springs 114Aand 114B, of the type described in connection with FIGS. 4-6. FIG. 7illustrates that the spring 114A has deflected beams (e.g., 116). Theorientation of the deflected beams indicates that the mirror 24 is beingpulled at flange 112A (left side of the mirror out of the page) andpushed at flange 112B (right side of the mirror into the page).

[0039] As in the case of the fast mirror 30, the motion of the slowmirror 24 is controlled by springs. That is, the springs 114 improve themotion of the mirror slider components 108, 105, and 110, which improvesthe motion imparted to the mirror flanges 112. The configuration of FIG.7 has symmetric actuation imparted by the comb drives 100 to produceimproved mirror motion.

[0040]FIG. 8 is an enlarged view of the bottom portion of the slowmirror 24. The figure illustrates the torsion bar 92B. The torsion bar92B may be connected to a conventional pin and staple hinge 130.

[0041]FIG. 8 also illustrates the mirror flange 112A, which includes abox frame 122 at its terminal end. The second transverse member 110 ofthe mirror slider includes a T-shaped termination member 124, which ispositioned over the bottom link of the box frame 122. The T-shapedtermination member 124 insures that the second transverse member 110 andthe mirror flange 112 stay assembled. A similar linkage mechanism isused between the fast mirror 30 and its slider 73. Note that the mirrorslider components 105, 108, and 110 are suspended over the substrate 90,allowing controlled motion.

[0042]FIG. 8 also illustrates a portion of each individual comb drive100A and 100B. Comb drive segment 131 of comb drive 100B is electricallyconnected to comb drive segment 132 of comb drive 100A. Similarly, combdrive segment 134 of comb drive 100B is electrically connected to combdrive segment 133 of comb drive 100A. If a voltage is applied to combdrive segments 133 and 134, the mirror slider pushes the mirror flange112A into the plane of the page, while the opposite mirror slider pullsthe opposite mirror flange out of the plane of the page, resulting in aclock-wise motion.

[0043] The physical components of the apparatus of the invention havenow been described. Attention presently turns to a more detaileddiscussed of attributes associated with various physical implementationsof the device. A detailed discussion of the operation of the device willalso follow. In particular, the following description will addressimprovements in the control signals used in connection with theapparatus and techniques to improve the optical output of the apparatusby compensating for mirror shape anomalies.

[0044] Standard MEM processing techniques may be used to fabricate themirrors and springs of the invention. In one embodiment of theinvention, two free-standing polysilicon layers are used to create themirrors (24, 30), comb-drives (70, 100) and tilt-up frames (66, 96). Thedevices may be fabricated with the Multi-User MicroelectromechanicalSystems Processes (MUMPs) described by K. W. Markus, et al., in “MEMSInfrastructure: The Multi-User MEMS Processes (MUMPs)”, Proc. SPIE, Vol.2639 (Micromachining and Microfabrication Process Technology, Austin,Tex., USA, 23-24, Oct. 5, 1995), p. 54-63. Similarly, the processingtechniques described in the previously referenced '297 patent may beutilized. After fabrication, the devices may be released in a 49%Hydroflouric (HF) acid solution and dried in a supercritical CarbonDioxide (CO₂) chamber. After release and drying, the chips may becovered with 50 nm of aluminum by blanket evaporation to enhance mirrorreflectivity. Overhanging polysilicon structures are preferably used toavoid electrical shorts caused by metal deposition. This design featurewas tested successfully on the single-chip scanner.

[0045] The mirrors (24, 30) and torsion beams (64, 92) have beenimplemented with 1.5 μm-thick polysilicon. The tilt-up frames,comb-drives and folded springs have been implemented with 3.5 μm-thickpolysilicon. The tilt-up frames are used to raise the mirrorsout-of-plane and hold them securely. The frames are connected to themirrors by torsional hinges and to the chip surface by pin-and-staplehinges, as illustrated in FIGS. 4 and 7. The frames and mirrors may have3 μm-diameter etch holes spaced on a 30 μm grid for fast release in HF.Each mirror, originally fabricated flat on the chip surface, may beassembled using a probe on a micropositioner. The probe is used to pushforward the lifters 68, 98 which are connected to the back of the frames62, 94. The mechanical stability of the scanning mirrors can be improvedby fixing the frame joints with epoxy.

[0046] As previously discussed, the mirrors are actuated by comb-drivesthat are connected to the mirrors through hinges near the chip surface.The comb-drives move in the plane of the chip. The folded springs (74,114) provide the majority of the stiffness for the actuator-mirrorsystem. All comb-drives used to actuate the mirrors can be operatedbi-directionally, i.e. two sets of comb teeth are used, one set pullingin the opposite direction of the other. At resonance, a mirror need onlybe driven in one direction, and the inertia of the system will cause itto oscillate nearly symmetrically about its equilibrium point. If amirror is operated below its resonant frequency, it is must be drivenbi-directionally to achieve maximum deflection.

[0047] As previously illustrated, the fast mirror 30 rotates about anaxis parallel to the chip surface, and the slow mirror 24 rotates aboutan axis perpendicular to the surface. The fast mirror 30 may beimplemented with a 65-by-500 μm rectangle flanked by two 500 μm-diameterhalf-circles, making the mirror nearly circular. In one embodiment, itrotates about its long (565 μm) axis, and has a resonant frequency of4.68 KHz (FIG. 4). Fast-mirror frequency-response curves were collectedfrom devices on several chips. Each mirror had a slightly differentresonant frequency, ranging from 4.54 KHz to 4.68 KHz.

[0048] All fast mirrors were driven at 4.6 KHz when used to generate thehorizontal component of a raster-scan. The device characterized in FIG.9 is from a single-chip display. The fast-mirror torsional hinges 64 maybe 50 μm×3 μm×1.5 μm, and the folded spring 74 may be 299 μm×3 μm×3.5μm, supporting opposing banks of 66 comb teeth, each 40 μm×3 μm×3.5 μm.The measured optical scan angle of the fast mirror is 15 degrees whenoperated at resonance, driven with a 36.1 V_(rms) sine wave and zero DCoffset. The slow mirror 24 may have the same shape as the fast mirrorbut may be elongated along its axis of rotation by the insertion of a253-by-565 μm rectangle to collect the light from the fast-mirror scan.The slow mirror 24 may be actuated symmetrically by two banks ofcomb-drives (100A, 100B), each driven with a triangular voltage waveformat 60 V_(pp) and zero DC offset. Driving the opposing comb-drives at 90degrees out-of-phase results in a net triangular-force waveform. Using atriangular-shaped waveform instead of a sinusoidal driving signalincreases the linear region of the slow-mirror scan.

[0049] The comb drives 100A, 100B for the frame-refresh (slow) mirror 24of FIG. 7 are used to produce a push-pull force on the frame-refreshmirror 24. The frame-refresh mirror 24 must be driven in both directionsbecause it is operating below its resonant frequency. It is advantageousfor the mirror angle versus time to follow a triangular waveformcentered about zero. By making a fast reversal of the scan direction ateach edge of the frame scan (at the peak or valley of a triangularwaveform), and holding a constant velocity over the majority of theframe, fast-scan lines can be easily projected with uniform spacing.Correction for non-linear velocity changes are not necessary.

[0050] The opposing comb drives 100A, 100B allow the use of piecewiselinear, symmetric triangle waves to achieve a triangular force waveformfor mirror actuation. If just one comb drive were used, the netelectrostatic force would be proportional to the square of the appliedvoltage. If a triangular waveform were applied to a single comb drive,the resulting force would not be piecewise linear. A triangular voltagewaveform applied to a mirror with the opposing comb drive design yieldsa net electrostatic force that is proportional to the input voltage (andphase-shifted). The optical modulation for the display need not bemodified to correct for non-linear motion of the mirror.

[0051] The slow-mirror folded springs 114 may be 600 μm=3 μm=3.5 μm. Thecomb tooth design is the same as that found on the fast mirror, except132 teeth are available to drive the mirror in each direction. The slowmirror deflects the optical beam through 15 degrees on an axisorthogonal to the fast mirror and has a resonant frequency of 1.14 KHz,as illustrated in FIG. 10.

[0052] The slow mirror 24 moves at a sub-harmonic frequency of the fastmirror 30. This simplifies the driving electronics for the opticalmodulator. There are an integer number of line-scan cycles in the imagerefresh mirror cycle.

[0053] The resolution of a raster-display is determined by bothmechanical-system issues and the optical quality of the mirror surfaces.The resonant frequency of the fast mirror limits the display resolutionby restricting the number of lines that can be scanned during the imagerefresh period. In visual display systems, ergonomics must be consideredwhen determining the image refresh rate. Factors that affect flickerperception include the location of the image in the visual field theaverage luminance of the display, and direction of the raster scan. Ahigh-quality scanning display should require an image refresh rate ofabout 100 Hz. Raster-scan images described herein make use of theleft-to-right and top-to-bottom portions of the fast and slow mirrorscans, respectively. Using the other half-cycle of the fast andslow-mirror scans boosts the mechanically-limited resolution by a factorof four.

[0054] The optical resolution is a function of the maximum optical scanangle divided by the angular divergence of the reflected laser beam, asdescribed below. Curvature of the mirror surface increases thedivergence angle of the reflected beam. Mirror curvature caused byactuation forces or stress gradients inherent in the fabrication processwill therefore severely degrade the scan resolution if left uncorrected.

[0055] The laser 40 of FIGS. 2 and 3 may be a 5 mW, 633 nm Helium-Neon(HeNe) laser source. Unlike spatially incoherent sources, nearly all ofa laser's optical power can be focused onto the surface of amicro-scanning mirror, and eventually to the display screen 36 (FIG. 1).This simplifies the transfer of high-optical power density throughmicro-optical systems. In addition, optical analysis is simplified bythe narrow spectral and uniform phase characteristics of the laser. Thefollowing discussion assumes that the light source is monochromatic andspatially coherent with a transverse Gaussian distribution.

[0056] Within the Gaussian beam propagation model, the best resolutionfor an optical scanner is obtained by positioning the waist of theincident optical beam at the surface of the micromirror and the imageplane in the far-field. A number of different geometries will achievethe same resolution as this configuration, but none are likely toimprove performance. The standard rule of thumb for analog (scanning)cathode ray tube designs is that neighboring pixels should be separatedby the Full Width at Half Maximum (FWHM) of their intensity. Given thiscriterion, the number of resolvable spots for a one-dimensional scanneris given by: $\begin{matrix}{N = \frac{{\alpha\pi\omega}_{m}}{1.178_{\lambda}}} & \left( {{Equation}\quad I} \right)\end{matrix}$

[0057] where α is the optical scan angle, ω_(m) is the radius of theoptical beam waist on the mirror (in this discussion, optical beamradius always refers to the radius of the laser beam at its 1/e²intensity value), and λ is the optical wavelength. To improve theresolution, it is necessary to increase the product αω_(m). Mirrors thataccept a large optical beam and rotate through large angles are desired.

[0058] Equation I represents an ideal scanning mirror that is perfectlyflat and of infinite extent. Curvature and imperfections of the opticalsurface, as well as the finite size of a real mirror, will reduce theresolution. Stress-gradient-induced mirror curvature is dominant amongthese. In the disclosed two-mirror display system, mirror curvature willtypically cause an increase in the area of the far-field optical beam bya factor of more than 1000 if left uncorrected. By approximating thecurved-mirror profile as parabolic, one can calculate the increase inthe far-field beam size and the proportional reduction in resolution.This may be expressed as the ratio M of the actual optical beam radiusto the theoretical beam radius for an ideal, flat mirror of infiniteextent $\begin{matrix}{M = {\frac{1}{{f}_{\lambda}}\sqrt{\left( f_{\lambda} \right)^{2} \cdot \left( {\pi\omega}_{m}^{2} \right)^{2}}}} & \left( {{Equation}\quad {II}} \right)\end{matrix}$

[0059] where f is the focal length of the mirror and ω_(m) is the radiusof the incident optical beam waist on the mirror.

[0060] To optically compensate for the curvature of a micromirror, itsradius of curvature, or equivalently, the focal length of the mirror,must be found. To do this, the far-field optical beam radius is measuredfor several laser beam waist sizes on the mirror. Dividing the measuredfar-field optical beam radius by the theoretical far-field optical beamradius of a perfectly flat, infinitely large mirror yields the value ofM. Typical examples of experimentally determined values of M forscanners of the invention are plotted in FIG. 11. Equation II is fittedto these points with f as a fitting parameter. Equation II is, strictlyspeaking, only valid for a mirror of infinite extent, but may be used tofit data for the following reasons. First, for small incidentbeam-waist-radii less than three times the mirror radius, there iseffectively no diffraction off the mirror edges. Second, larger incidentoptical beams are greatly expanded by the mirror curvature in thefar-field, causing the relative influence of the aperture effect to besmall.

[0061] Testing with polysilicon mirrors indicates that resolution lossdue to curvature is small for an incident beam waist less than 50 μm.Equation I, however, shows that larger beam radii, and thus largermirror sizes, are desired to increase resolution. Increasing the radiusof the laser beam on the mirror causes an increased sensitivity tomirror curvature. The mirror characterized in FIG. 11 has anedge-to-center bow of approximately 1.2 μm, which is enough to cause anincrease in the far-field optical beam area by a factor of 506 when themirror is filled with a 250 μm-radius waist. Stress gradients in thepolysilicon, inherent to the fabrication process, are the suspectedcause of curvature in the mirror. While it may be difficult to flattenthe mirror by entirely eliminating stress gradients from thepolysilicon, an optical correction is achieved in accordance with theinvention.

[0062] Once the focal length is known, the mirror curvature can beoptically canceled by appropriately forming the phase front of theincident optical beam. Using the Gaussian beam propagation model, a twoor three-lens system can be designed to pre-form the laser beam suchthat the waist of the reflected beam is at the surface of the secondmirror in a two-mirror system. Orthogonal axes on each mirror can beindependently optimized with cylindrical optics. Curvature is thedominant factor in reducing resolution. By correcting for curvature in atwo-mirror system, the radius of the optical beam in the image plane isreduced by a factor typically between 30 and 40. This brings themeasured far-field optical beam size to within 12% of its diffractionlimit (including the aperture effect, see below) simultaneously on bothaxes of a single-chip scanner. Once the mirror curvature is opticallycompensated in accordance with the invention, the aperture effect of themirror becomes significant in determining the diffraction-limitedfar-field optical beam size. Truncation of the Gaussian laser beam atthe mirror broadens the far-field intensity distribution and causes sidelobes to appear about the central intensity maximum, as illustrated inFIG. 12. The relative power in the central and side-lobes is dependentupon the ratio of the incident optical beam radius to the mirror radius.As stated above, if the radius of the mirror is at least three times theradius of the optical beam, the aperture effect of the mirror becomesnegligible. Increasing the radius of the incident optical beam reducesthe central lobe width of the diffraction patterns. A larger incidentbeam radius also increases the power in the side-lobes, which isundesirable for display applications. In addition, reflection off of thetilt-up frame surrounding the mirror increases with incident opticalbeam size, causing artifacts in the raster-scanned image. Taking thesefactors into consideration, a 250 μm-incident beam radius may be chosen,roughly equivalent to the fast mirror size. For this case, minimalreflection off of the frame is observed, and the power in the side lobesis low. The central lobe, however, expands by about 49% compared to anun-apertured beam, as demonstrated in FIG. 12, and this expansion leadsto a proportional reduction of the number of resolvable spots comparedto the infinite-mirror case (equation I).

[0063] Actuation forces on the mirrors will also influence theresolution. The actuators disclosed herein are connected directly to thebottom edges of the mirrors through hinges. The comb-drives induce atorque about the mirrors' torsional hinges, with the mirror surfaceacting as the moment arm. The applied force at the edge of the mirrorcauses bending of the optical surface that varies with the rotationalposition of the mirror. FIG. 13 documents the effect of mirror bendingon the far-field optical beam size. The optical beam size at zerodeflection is 400 μm, close to the 361 μm-predicted diffraction-limitfor a 250 μm beam on a 250 μm mirror and a 30 cm-focal-length outputlens. Through the entire range of actuation shown in FIG. 13, thedifference between the optical beam radii on perpendicular axes in thefar-field remained less than 15%, indicating bending along both axes ofthe mirror surface. Connecting the comb-drives to an independent leverarm that is attached to the mirror near the torsional hinges will remedythe problem of curvature induced by static actuation forces.

[0064] Inertial and dynamic forces can also play a role in bending themirror surface. Preliminary data suggest that dynamic curvature of thefast mirror has a measurable influence on the far-field beam size whenthe scanner is operated at resonance.

[0065] The preceding mechanical and optical analyses were used in thedesign and testing of individual micromachined scanners. The two-mirrorraster-scanner design relies on information collected from individualmirrors. The following discussion focuses on the results fromsingle-chip and dual-chip raster scanners.

[0066] In the single-chip design, the fast and slow mirrors arepositioned opposite each other, separated by an optical path length of936 μm. One method of optical correction for the mirror curvaturesrequires that the incident optical beam form a virtual waist behind thefast mirror. The fast mirror is tilted back approximately 3 degrees fromthe perpendicular, allowing the converging incident laser beam to reachthe mirror without grazing the chip surface. The slow mirror is normalto the chip surface. The stationary output mirror accepts light from theslow mirror and re-directs it through the output optics to the displayscreen or camera.

[0067] A 5.02 cm-focal-length lens, followed by a cylindrical concavelens with focal length 833.3 cm and a 10 cm-focal-length lens correctfor the combined curvature of the two-mirror system. The output mirror,made of single-crystal silicon, has negligible curvature. The opticalsurface of the output mirror must be within approximately 50 μm of thechip surface to capture the full raster scan, and the top of the mirrormust tilt away from the slow mirror to direct the light off-chip. Toproduce a sharp edge at the base of the mirror, the silicon was etchedin a KOH bath along a crystalline plane at 54.7 degrees with respect tothe polished mirror surface. A micropositioner orients and holds theoutput mirror in place. The output optics consist of a 10cm-focal-length lens and additional optics used to photograph the scan.Due to the geometry of the camera, two 30 cm-focal-length lenses in an4-f configuration were needed to transfer the image, found at the backfocal plane of the 10 cm lens, into the camera. After exiting the second30 cm-focal-length lens, the light falls directly onto the film. Directimaging of the display onto film eliminates speckle, commonly found inlaser projection systems. Speckle is caused by optical interference inthe light scattered from a projection screen due to roughness of thescreen surface.

[0068] To increase the rigidity of the tilt-up frames, all stationaryhinge joints are preferably epoxied, with the exception of two joints atthe base of the slow mirror frame. Epoxy was not applied to thesestationary hinges because the adhesive could potentially spread tonearby actuator members, causing them to freeze in position.

[0069] An acousto-optic modulator in the beam path adjacent to the lasersource (element 42 in FIGS. 2 and 3) switches the light on-and-off witha signal that is synchronized to the mirror driving voltages. Theacousto-optic modulator turns off the light in a narrow region (about 7%of the display width) at each edge of the horizontal scan. Thisnon-linear turnaround region of the fast-mirror is not used for imagedisplay. A mechanical shutter 46 selects a half-cycle of the slow mirrorto expose the film. The corrected optical beam size in the center of theimage plane was within 12% of the theoretical diffraction-limitedprediction. The smallest pixel size is at the center of the display,with no voltage applied to the actuators. If the display were filledwith pixels of this size, its resolution would be 176 by 176. Accountingfor the turn-around region on the horizontal scan, the resolution is 151by 176. However, the pixel size varies according to mirror angle.

[0070] The highest-resolution region in the image plane is a rectanglerunning the full height of the display and covering about 25% of thehorizontal scan width. In this portion of the display, there is littledeviation of the optical beam size from its minimum. Outside of thisarea, the scan lines become blurred. At the extreme edges of thedisplay, the far-field beam size expands by roughly a factor of 2.5. Bylinear approximation, the laser beam expands in size by an averagefactor of 1.75 over 75% of the display. The horizontal displayresolution can be approximated based on average pixel size to be 0.86*176*(0.25+0.75/1.75)=102 pixels. This average pixel size is used todefine the horizontal line spacing because the optical beam isessentially circularly symmetric. Therefore, the vertical resolutionbased on average pixel size is approximately 176*(0.25+0.75/1.75)=119,because the fast and slow mirrors rotate through the same angle. Thereis effectively no resolution loss to turn-around regions in theslow-mirror scan because it is driven by a triangular waveform.

[0071] Several raster-scanned images were photographed to demonstratethe display system. Dynamic effects, such as jitter and wobble, degradethe image quality. Jitter in the slow mirror causes bright horizontallines, resulting from overlapping line scans. Three effects play a rolein expansion of the far-field optical beam size at the end of the fastmirror scan line: static mirror deformation, dynamic mirror deformation,and wobble of the fast mirror. Wobble amplitude in the single-chipdesign appears to be less than the average pixel width. Sub-harmonicwobble was found in the two-chip raster-scanner, which is discussedbelow.

[0072] A second optical raster-scanning system was tested independentlyof the single-chip scanner. The two-chip raster-scanner makes use of twofast mirrors oriented with orthogonal scan axes, as shown in FIG. 3. Oneof the fast mirrors performs the same function as the slow mirror in thesingle-chip design. In this embodiment, none of the tilt-up frames wereepoxied. The fast and slow-moving mirrors were operated at 5.3 and 5.7degrees of optical deflection, respectively. Both mirror frames weretilted back with an angle of approximately 7 degrees from theperpendicular. The curvature-correction optics described in the previoussection are used with the exception of the cylindrical lens. An opticalassembly 60 with two 6.29 cm-focal-length lenses in a 4-f configurationis inserted between the mirrors to image the fast mirror onto theslow-moving mirror. These lenses could also be used to correct formirror curvature. The output optics consists of a 30 cm-focal-lengthlens. The camera is positioned at the back-focal-plane of the outputlens. The corrected far-field optical beam size in the image plane is17% larger than the predicted diffraction limit. Compared to thesingle-chip design, a proportionally smaller region of the image isaffected by curvature due to actuation because the scan angle issmaller. The resolution based on average pixel size is estimated to be61 by 65 pixels.

[0073] Jitter of the slow-moving mirror in the two-chip system is lessprominent than in the single-chip display. The basic mechanical designof the fast mirror, when used as a slow-moving mirror in the two-chipdisplay, may have superior jitter characteristics over the slow mirrordesign in the single-chip display. The fast-mirror wobble amplitude inthe two-chip display, however, is significantly greater than thecorresponding wobble amplitude found in the single-chip design. This maybe due to more motion of the supporting frames because they were notepoxied in place. The wobble amplitude is greater than the horizontalline separation and the wobble frequency is lower than the rotationalfrequency of the fast mirror. When the system is operating as a display,the acousto-optic modulator selects the upper half-cycle of eachline-scan, selectively switching the light off as the mirror wobbles.Mirror wobble in the two-chip system also interleaves the scan lines,causing the horizontal lines from top-to-bottom to be drawn out ofsequence. To display the raster-image data in the correct sequence,every-other line-scan half-cycle was selected by the acousto-opticmodulator. To maintain proper line spacing in this situation, theslow-scanning mirror frequency must be reduced by half.

[0074] In sum, an improved surface-micromachined raster-scanning displayhas been disclosed. The apparatus has been implemented with a resolutionof 151 by 176 pixels, and an average resolution of 102 by 119 pixels ina single-chip system. The tilt-up polysilicon mirror design allows forlarge mirror size and deflection, both shown to be necessary forhigh-resolution displays. Mirror curvature was found to be the primaryfactor that reduces resolution in micromachined scanners. The mirrorcurvature was characterized by measuring the far-field intensitydistributions for a series of incident optical beam sizes and fittingthe data to a theoretical curve. Information gathered from thistechnique determines the configuration of curvature-correcting opticsthat pre-form the optical beam incident on the scanners. This methodsuccessfully reduced the laser beam radius in the image plane of thesingle-chip raster scanner by more than an order of magnitude, bringingit to within 12% of the theoretically-predicted diffraction limit.

[0075] Once the static mirror curvature was corrected, the factorslimiting resolution and image quality were actuation-induced bending,jitter and wobble of the scanning mirrors. Modifying the fast mirrordesign by removing the direct connection of the comb-drive to the bottomof the mirror is expected to increase the resolution of the display.Deformation of the mirror can be avoided by connecting the comb-drive tothe mirror through separate polysilicon beams that attach to the edgesof the mirror near its rotational axis.

[0076] To reach VGA resolution, the mirrors must increase in size andtilt-angle, and the resonant frequency of the fast mirror should beboosted. Maximizing the mechanical force output of the comb-driveactuators will be required to reach a sufficiently high resonantfrequency. It is likely that stiffening of the fast-mirror surface toreduce dynamic bending will also be necessary.

[0077] Those skilled in the art will appreciated that the disclosedtechnology can be used in light-weight, low-power, and low-cost videodisplays. For a flicker-free video display, the slow mirror shouldoperate between 30-100 Hz. The video line-scan rate should be between30-100 kHz. In the demonstrated single-chip display, one line is drawnfor each half-cycle of the fast mirror, and no lines are drawn duringhalf of the slow mirror cycle. If information is displayed during bothhalf-cycles of the fast and slow mirrors, the effective line-scan rate(the number of lines drawn during one slow mirror cycle) increases by afactor of four. A 10 kHz fast-mirror that has already been demonstratedcould produce an equivalent line-scan rate of 40 kHz, which issufficient to display video. The following mechanical enhancements willimprove system performance: increasing rotational angle and size of themirror enables higher resolution displays, increasing the stiffness ofthe mirror springs increases the line-scan rate, and increasing themirror stiffness ensures uniform pixel size across the display.

[0078] Those skilled in the art will appreciate that a variety oftechniques may be used to measure mirror curvature. A mirror may beplaced in a device designed to measure the mirror curvature. Thefar-field characteristics of an optical beam reflected off of amicro-mirror can be used to compute the mirror curvature. Theinstruments used to measure the far-field optical beam size may beplaced anywhere in the far-field (this can be advantageous) at a knowndistance from the mirror, and only one measurement may be required. Fromthese measurements, the mirror curvature can be theoretically extractedand used to design corrective optics. The corrective optics may beplaced before, between, or after the mirrors. In some cases it may beadvantageous to place lenses in two or all three locations. In the caseof a micro-display system, it may be advantageous to place all of theoptics after the mirror system to minimize the number of micro-lensesthat need to be mounted on the chip.

[0079] It is not necessary to remove a micro-mirror from the displaysystem to measure micro-mirror curvature. Corrective optics can beoptimized for the curvature of an individual mirror by adjusting lenspositions or adjusting the placement of the projection screen in thedisplay system, using the display system laser as the measurement beam.This process finds the mirror curvature and tunes the corrective opticsat the same time, potentially simplifying the process of building aworking display.

[0080] Placement of bulk mirror-curvature correction optics that lieexternal to the microscopic system may be used in manufacturingmicro-displays. In such a case, the light source and mirrors areassembled on a substrate and are incorporated into a package, withoutthe need to customize the optics in the package. Mirror curvaturecorrection is performed later with a macroscopic lens. Mirror curvaturecan be corrected by appropriate selection of the output optics, optimumplacement of the display screen, or a combination of the two.

[0081] There are numerous causes of mirror curvature, includingstress-gradients, thermal expansion and contraction, static, dynamic,and inertial forces. A system can be engineered to cancel the combinedeffect of mirror curvature in both mirrors without inclusion of externalcurvature-correcting optics. A convex mirror immediately following aconcave mirror with the same absolute radius of curvature can be used tocancel the effect of mirror curvature. Similarly, a concave mirrorfollowed by a convex mirror with the same absolute radius of curvaturecancels the curvature effect.

[0082] In micromachined systems, curvature due to stress-gradients isoften uniform over the small region of the substrate on which thedisplay is fabricated. By fabricating one mirror with its opticalsurface facing down, and the other mirror with its optical surfacefacing up (before assembly), the mirrors have opposite concavity afterrelease. After release and assembly, one mirror is convex and the otherconcave. The divergence or convergence that the first mirror induces inthe reflected optical wavefront is largely canceled after reflectionfrom the second mirror.

[0083] The foregoing description, for purposes of explanation, usedspecific nomenclature to provide a thorough understanding of theinvention. However, it will be apparent to one skilled in the art thatthe specific details are not required in order to practice theinvention. In other instances, well known circuits and devices are shownin block diagram form in order to avoid unnecessary distraction from theunderlying invention. Thus, the foregoing descriptions of specificembodiments of the present invention are presented for purposes ofillustration and description. They are not intended to be exhaustive orto limit the invention to the precise forms disclosed, obviously manymodifications and variations are possible in view of the aboveteachings. The embodiments were chosen and described in order to bestexplain the principles of the invention and its practical applications,the thereby enable others skilled in the art to best utilize theinvention and various embodiments with various modifications as aresuited to the particular use contemplated. It is intended that the scopeof the invention be defined by the following claims and theirequivalents.

What is claimed is:
 1. A method of operating a micromechanical scanningapparatus, said method comprising the steps of: identifying a radius ofcurvature value for a micromechanical mirror; and modifying a laser beamthat impinges upon said micromechanical mirror so as to compensate forsaid radius of curvature value so as to improve the optical resolutionof said micromechanical scanning apparatus.
 2. The method of claim 1wherein said identifying step includes the steps of: acquiring ameasured far-field optical beam radius for a laser beam reflected fromsaid micromechanical mirror; dividing said measured far-field opticalbeam radius by a theoretical far-field optical beam radius reflectedfrom an ideal mirror to yield a ratio value M; curve fitting ananalytical expression for M to experimental data for M with focal-lengthas a fitting parameter; and multiplying said focal-length of said curvefitting step by two to establish said radius of curvature.
 3. The methodof claim 2 wherein said dividing step includes the step of dividing saidmeasured far-field optical beam radius by a theoretical far-fieldoptical beam radius from a perfectly flat, infinitely large theoreticalmirror to yield said ratio value M.
 4. The method of claim 1 whereinsaid modifying step includes the step of optically modifying said laserbeam to compensate for said radius of curvature.
 5. The method of claim4 wherein said modifying step includes the step of reshaping the phasefront of said laser beam to compensate for said radius of curvature. 6.The method of claim 1 wherein said modifying step includes the step ofoptically modifying said laser beam within said micromechanical scanningapparatus.
 7. The method of claim 1 wherein said modifying step includesthe step of optically modifying said laser beam outside of saidmicromechanical scanning apparatus.
 8. The method of claim 7 whereinsaid modifying step includes the step of optically modifying said laserbeam with macroscopic lenses.
 9. The method of claim 7 wherein saidmodifying step includes the step of optically modifying said laser beamthrough positioning of a display screen.
 10. The method of claim 7wherein said modifying step includes the step of modifying said laserbeam with a second micromechanical mirror with a radius of curvaturevalue that is opposite said radius of curvature value for saidmicromechanical mirror.
 11. The method of claim 1 further comprising thestep of synchronizing a first micromechanical mirror with a secondmicromechanical mirror with a modulated light source to produce adisplayed image.
 12. The method of claim 11 further comprising the stepof operating said modulated light source to produce grey-scale imageswithin said displayed image.
 13. The method of claim 11 furthercomprising the step of projecting said displayed image onto the retinaof an eye.
 14. The method of claim 11 wherein said secondmicromechanical mirror moves at a sub-harmonic frequency of said firstmicromechanical mirror.
 15. An optical scanning device, comprising: afirst micromechanical mirror; a first micromechanical drive mechanism; afirst micromechanical spring attached to said first micromechanicaldrive mechanism to control the motion applied to said firstmicromechanical minor from said first micromechanical drive mechanism; asecond micromechanical mirror; a second micromechanical drive mechanism;and a second micromechanical spring attached to said secondmicromechanical drive mechanism to control the motion applied to saidsecond micromechanical mirror from said second micromechanical drivemechanism.
 16. The apparatus of claim 15 wherein said secondmicromechanical drive mechanism is implemented as a set of comb drivesthat control the position of two points of said second micromechanicalmirror.
 17. The apparatus of claim 15 wherein said first micromechanicaldrive mechanism is implemented as a single comb drive that controls theposition of a point of said first micromechanical mirror.